All brokers do not limit the trading volume but there are instances that they control the volume because of the trading balance available.

I don't think so, because my broker doesn't limit anything as long as the equity is intact.

Yes, there are many brokers who limit the volume of trade. So, make sure to check your broker before making a decision.

There are some brokers who limit the volume of trade for the security purposes. But I don't think if it is helpful.